A Look at Some 1st Grade Common Core Problems

A Look at Some 1st Grade Common Core Problems

Common Core… Time to Dive In

My goddaughter is entering first grade this year.  We all heard of Common Core Mathematics.  My introduction to Common Core was an unfortunate one: a Facebook post where a student was marked wrong because a drawing wasn’t done correctly.  However, since Common Core in the United States is a reality and since I anticipate being asked for help with the math homework, I’m going to need to check out what is being taught in first grade. 

I’m going to highlight some types of problems that might be encountered in a first grade class. 

I want to thank A+ Plus Math Coach, link: http://www.aplusmathcoach.com for posting worksheets that cover Common Core math from grades K-5.  Most of the type of problems I will talk about in today’s blog post is based of these worksheets. 

Math Skills Emphasized

* Place Value, Tens and Ones

* Addition

* Subtraction

* Simple Graphs

* Counting

It would help if the student knows all the addition facts involving 0 to 10.  Yes, that addition table we memorized as kids is still helpful.

For a full list of skills (it’s a long one), click here:  http://www.corestandards.org/Math/Content/1/OA/

Counting Problems

Sample Problem 1:  How many balloons are in the box?

 This is fairly simple, we should count 12 balloons.

Other counting problems have students arranging objects into groups of ten when possible. 

Sample Problem 2:  Rhonda has six pieces of candy and Rita has eight pieces of candy.  How many pieces of candy do they have together?

Illustrated is the candy Rhonda (dark brown pieces) and Rita (tan pieces) have.  One exercise to have the student group the objects in tens when possible.  For this problem, we can have one group of ten pieces while four pieces are left over.  1 ten and 4 ones make 14. 

Adding and Subtracting

Most adding and subtracting problems should be straight forward.  As I mentioned before, it will help greatly if the student knows their addition tables.

Algebra, Without the Symbols

Some problems are presented as they come from first level algebra.  Instead of “Solve for X”, it’s “Solve for the blank space”.

Sample Problem 3:  Fill in the blank:  5 + ___ = 8. 

If the student knows their addition, the student would come up with 3 as the answer.  Sometimes, the problem states “You have 5 units.  How many units do you need to make 8 units?”

Sample Problem 4:  Think of the problem 8 + __ = 10 to solve 10 - ___ = 8.

“You have 8 units.  How many units do you need to make 10 units?”

“You have 10 units, how many units do you need to give away to have 8 units left?”

The answer to both questions is 2.  If someone finds a better way to explain this, please post this in the comments. 

Sample Problem 5:  The following sentence is false:  5 + 7 + 9 = 16.  Remove one of the numbers on the left to make the sentence true.

The goal here is to find the two addends in the sentence that add up to 16.  From the three possibilities:

5 + 7 = 12, no

5 + 9 = 14, no

7 + 9 = 16, yes

Since 7 and 9 are required, the 5 needs to be removed.

Doubles

One concept that may be introduced is the concept of additive doubles.  Simply put, the doubles are:

1 + 1 = 2	2 + 2 = 4	3 + 3 = 6	4 + 4 = 8	5 + 5 = 10
6 + 6 = 12	7 + 7 = 14	8 + 8 = 16	9 + 9 = 18	10 + 10 = 20

How can this come into play?  Some adding problems can be labeled as double plus one and double minus one. 

Sample Problem 6:  7 + 8

This can be seen as a double plus one problem. Note we can break the 8 into 7 + 1, then we have 7 + 7 + 1 (a double addition of 7). 

The thought process:

If 7 + 7 = 14 (double 7 fact)

Since 8 is 1 more than 7, add 1 to 14:

14 + 1 = 15.

An alternate strategy is the doubles minus one strategy. 

Start by recognizing that 8 + 8 = 16 (double 8 fact)

Since 7 is 1 less than 8, subtract 1 from 16:

16 – 1 = 15

This a strategy that facilitates mental math.

For video explanation of doubles, click on this link from Stephanie K:   https://www.youtube.com/watch?v=mbKkasLm5DY or from Bob Kowalec:  https://www.youtube.com/watch?v=elj4aup0wJk 

Graphs and Polls

I saw several problems that would require students to read graphs. 

Sample Problem 7:  Look at the table below, as a classroom of students in Mrs. Roberts said what their favorite toy is.  Mrs. Roberts tallies the results in the box below:

What is the most popular toy?  How many students participated in the poll?  (and similar questions)

This type of problem encourages counting and reading graphic representation of polls.  (Answers:  video game, 3 + 6 + 7 = 16)

Final Remarks

Other problems that I saw included requiring students to mentally add and subtract 10, and compare numbers between 10 and 99 using place value (compare tens digit first, then if they are the same compare the ones digit first). 

This is not going to be every problem that could be presented in a first grade Common Core math class, but I wanted to get an idea of what is taught in the classrooms.  I don’t know how much different first grade math is from today from when I was in first grade, which is 35 years ago. 

Eddie

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High Rollers: Game Show and Possible Sums with the TI-84 Plus

High Rollers:  Game Show and Possible Sums with the TI-84 Plus

If you have a group of numbers, what are the possible sums you can make?  We’re talking about combinations of 1, 2, to as many numbers you have.  This is one of the key elements of the classic game show High Rollers (1970s, 1987-1988), a dice rolling game based on Shut The Box. 

To whet your appetite, click on the links below to see classic episodes (the links should be good as of 3/15/2017).  The first two links are from episodes from the 1978-1980 series with Alec Trebek (with facial hair) and the last two links are from episodes from the 1987-1988 series with Wink Martindale. We’ll get to the game show later in this blog entry. (no ownership implied, these are from other YouTube accounts)

https://www.youtube.com/watch?v=nsxQoDM0rd0&t=1172s

https://www.youtube.com/watch?v=urzJINgMu3E

https://www.youtube.com/watch?v=j951e0r0EB8

https://www.youtube.com/watch?v=OeD__GYvZZk

The Program POSSUMS

The program POSSUMS calculates all possible sums created by a set of numbers (2, 3, or 4).  With n numbers available, there are 2^n – 1 possible sums.

For n = 2, with let A and B represent the numbers.   There are 2^2 -1  = 3 possible sums:

A, B, A + B

For n = 3 (A, B, C), there are 2^3 – 1 = 7 possible sums:

A, B, C, A + B, A + C, B + C, A + B + C

For n = 4 (A, B, C, D) there are 2^4 – 1 = 15 possible sums:

A, B, C, D, A + B, A + C, A + D, B + C, B + D, B + C, A + B + C, A + B + D, A + C + D, B + C + D, A + B + C + D

The program POSSUMS allows all possible sums, including repeats.

TI-84 Plus Program POSSUMS

Menu("SUMS FROM AVAIL. NUMBERS","2",2,"3",3,"4",4)

Lbl 2

Prompt A,B

{A,B,A+B}→L₁

Goto 5

Lbl 3

Prompt A,B,C

{A,B,C,A+B,A+C,B+C,A+B+C}→L₁

Goto 5

Lbl 4

Prompt A,B,C,D

{A,B,C,D,A+B,A+C,A+D,B+C,B+D,C+D,A+B+C,A+C+D,A+B+D,B+C+D,A+B+C+D}→L₁

Goto 5

Lbl 5

SortA(L₁)

Pause L₁

Examples

3 Numbers:  A = 2, B = 3, C = 5

Result:  {2, 3, 5, 5, 7, 8, 10}

Notes:  There are two 5s, meaning 5 can be made by two combinations (5, 2 + 3)

4 Numbers:  A = 1, B = 6, C = 7, D = 9

Result:  {1, 6, 7, 7, 8, 9, 10, 13, 14, 15, 16, 16, 17, 22, 23}

Notes:  7 can be made two ways (7, 6 + 1); 16 can be made two ways (7 + 9, 1 + 6 + 9)

The Game Show High Rollers

 

High Rollers was a game show that aired in three series: 1974-1976, 1978-1980, and 1987-1988.  The premise of the game was to clear as many numbers, ranging from 1 to 9.  In the original 1974-1976 series, each number was attached to a prize.  In the more famous 1978-1980 and 1987-1988 series, the numbers were aligned (seemingly at random) on a 3 x 3 grid.  Each column represented a prize or a group of prizes. 

In the main game there are two contestants.  You would win by either rolling the last number off the board or most likely, force your opponent to roll a number that can’t be cleared.  Obviously the total on the dice is used to clear numbers.  For example, a roll of a 6 (the total counts, not the pips on the individual dies), can clear any of the following combinations: 6 itself, 1 and 5, 2 and 4, or 1 and 2 and 3.  Starting with the 1978 series, rolling doubles earned the contestant an insurance marker, basically an extra life.

Winning two games entitled the champion to play the Big Numbers.  The object remained the same, get rid of the numbers 1 to 9 for a major cash prize or car.

One thing to note:  unlike Shut the Box, High Rollers offered no provision should the last number remaining on the board be a 1.

Below are all the possible combinations that can be cleared with each roll.  There are 61 combinations.  Statistically, rolling a 7 is the most likely event, followed by 6 or 8.  However, the most powerful rolls are 12, followed by 11, then 10. 

All the Possible Combos in High Rollers

Total	Combinations that can be Cleared
2	2
3	3, 1-2
4	4, 1-3
5	5, 1-4, 2-3
6	6, 1-5, 2-4, 1-2-3
7	7, 1-6, 2-5, 3-4, 1-2-4
8	8, 1-7, 2-6, 3-5, 1-2-5, 1-3-4
9	9, 1-8, 2-7, 3-6, 4-5, 1-2-6, 1-3-5, 2-3-4
10	1-9, 2-8, 3-7, 4-6, 1-2-7, 1-3-6, 1-4-5, 2-3-5, 1-2-3-4
11	2-9, 3-8, 4-7, 5-6, 1-2-8, 1-3-7, 1-4-6, 2-3-6, 2-4-5, 1-2-3-5
12	3-9, 4-8, 5-7, 1-2-9, 1-3-8, 1-4-7, 1-5-6, 2-3-7, 2-4-6, 3-4-5, 1-2-3-6

Let’s have some fun,

Eddie

This blog is property of Edward Shore, 2017